Citation

BibTex format

@inproceedings{Briol,
author = {Briol, F-X and Oates, CJ and Girolami, M and Osborne, MA},
pages = {1162--1170},
title = {Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees},
url = {http://arxiv.org/abs/1506.02681v3},
}

RIS format (EndNote, RefMan)

TY  - CPAPER
AB - There is renewed interest in formulating integration as an inference problem, motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoreticalanalysis. An important challenge is to reconcile these probabilisticintegrators with rigorous convergence guarantees. In this paper, we present the first probabilistic integrator that admits such theoretical treatment, called Frank-Wolfe Bayesian Quadrature (FWBQ). Under FWBQ, convergence to the true value of the integral is shown to be exponential and posterior contraction rates are proven to be superexponential. In simulations, FWBQ is competitive with state-of-the-art methods and out-performs alternatives based on Frank-Wolfe optimisation. Our approach is applied to successfully quantify numerical error in the solution to a challenging model choice problem in cellular biology.
AU - Briol,F-X
AU - Oates,CJ
AU - Girolami,M
AU - Osborne,MA
EP - 1170
SP - 1162
TI - Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees
UR - http://arxiv.org/abs/1506.02681v3
UR - https://papers.nips.cc/paper/5749-frank-wolfe-bayesian-quadrature-probabilistic-integration-with-theoretical-guarantees
UR - http://hdl.handle.net/10044/1/53208
ER -